Problem: Reduce to lowest terms: $- \dfrac{7}{9} \div - \dfrac{5}{9} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{5}{9}$ is $- \dfrac{9}{5}$ Therefore: $ - \dfrac{7}{9} \div - \dfrac{5}{9} = - \dfrac{7}{9} \times - \dfrac{9}{5} $ $ \phantom{- \dfrac{7}{9} \times - \dfrac{9}{5}} = \dfrac{-7 \times -9}{9 \times 5} $ $ \phantom{- \dfrac{7}{9} \times - \dfrac{9}{5}} = \dfrac{63}{45} $ The numerator and denominator have a common divisor of $9$, so we can simplify: $ \dfrac{63}{45} = \dfrac{63 \div 9}{45 \div 9} = \dfrac{7}{5} $